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A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C working together to finish the work?

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Number of days required by A and B to finish the work : 15 days 

Number of days required by A and B to finish the work : 12 days 

Number of days required by A and B to finish the work : 20 days

Work done by A and B in one day: \(\frac{1}{15}\)

Work done by B and C in one day: \(\frac{1}{12}\)

Work done by C and A in one day: \(\frac{1}{20}\)

Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by

(A + B) + (B + C) + (C + A) = 2(A + B + C) = \(\frac{1}{12}+\frac{1}{12}+\frac{1}{20}=\frac{12}{60}=\frac{1}{5}\)

Work done by A, B and C = \(\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}\)

∴ They can do the work in 10 days

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